Problem: Simplify the following expression and state the condition under which the simplification is valid: $t = \dfrac{z^2 - 14z + 48}{z^2 - 8z}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{z^2 - 14z + 48}{z^2 - 8z} = \dfrac{(z - 6)(z - 8)}{(z)(z - 8)} $ Notice that the term $(z - 8)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(z - 8)$ gives: $t = \dfrac{z - 6}{z}$ Since we divided by $(z - 8)$, $z \neq 8$. $t = \dfrac{z - 6}{z}; \space z \neq 8$